Читать книгу EEG Signal Processing and Machine Learning - Saeid Sanei - Страница 41

For coupling two neurons two integrate‐and‐fire neurons with mutual excitatory or inhibitory coupling have been described in [1]. The neurons with activation variables x_i for i = 1, 2, satisfy:

(3.1)

where ξ >1 is a constant, 0 < x_i < 1, and E_i (t) is the synaptic input to neuron i. Neuron i fires when x_i = 1 and hen resets x_i to 0. If cell j ≠ i fires at time t_j the function E_i is augmented to E_i (t) + E_s (t‐t_j ), where E_s is the contribution coming from one spike [1]. In an example in [1] this function is selected as:

(3.2)

where g and α are parameters determining the strength and speed of the synapse respectively and the factor of α ² in (3.2) normalizes the integral of E_s over time to the value g. In the considered cases the two neurons continue firing periodically when they are coupled together. Assuming that neuron 1 fires at times t = nT, where T is the period and n is an integer, while neuron 2 fires at t = (n − φ)T. Therefore, both neurons are firing at the same frequency but are separated by a phase φ. We wish to determine possible values of the phase difference φ and conditions under which they arise.